Trac #31722: turn is_field and is_integral_domain into cpdef function…

…s (completely doctested)

src/sage/rings/polynomial/multi_polynomial_ring_base.pyx

@@ -97,7 +97,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
             category = polynomial_default_category(base_ring.category(), n)
         sage.rings.ring.Ring.__init__(self, base_ring, names, category=category)
 
-    def is_integral_domain(self, proof = True):
+    cpdef bint is_integral_domain(self, proof=True) except -2:
         """
         EXAMPLES::
 

src/sage/rings/ring.pxd

@@ -8,6 +8,8 @@ cdef class Ring(ParentWithGens):
     cdef public object _zero_ideal
     cdef public object _unit_ideal
     cdef public object __ideal_monoid
+    cpdef bint is_field(self, proof=*) except -2
+    cpdef bint is_integral_domain(self, proof=*) except -2
 
 
 cdef class CommutativeRing(Ring):

src/sage/rings/ring.pyx

@@ -780,7 +780,7 @@ cdef class Ring(ParentWithGens):
             return True
         raise NotImplementedError
 
-    def is_field(self, proof = True):
+    cpdef bint is_field(self, proof=True) except -2:
         """
         Return ``True`` if this ring is a field.
 
@@ -920,7 +920,7 @@ cdef class Ring(ParentWithGens):
         """
         return False
 
-    def is_integral_domain(self, proof = True):
+    cpdef bint is_integral_domain(self, proof=True) except -2:
         """
         Return ``True`` if this ring is an integral domain.
 
@@ -1782,7 +1782,7 @@ cdef class IntegralDomain(CommutativeRing):
         CommutativeRing.__init__(self, base_ring, names=names, normalize=normalize,
                                  category=category)
 
-    def is_integral_domain(self, proof = True):
+    cpdef bint is_integral_domain(self, proof=True) except -2:
         """
         Return ``True``, since this ring is an integral domain.
 

src/sage/structure/element.pyx

@@ -4146,7 +4146,6 @@ cdef class FieldElement(CommutativeRingElement):
 
             sage: R.<x,y> = QQ[]
             sage: S.<a,b> = R.quo(y^2 + 1)
-            sage: S.is_field = lambda : False
             sage: F = Frac(S); u = F.one()
             sage: u.quo_rem(u)
             (1, 0)

src/sage/symbolic/ring.pyx

@@ -583,7 +583,7 @@ cdef class SymbolicRing(CommutativeRing):
         """
         return self.symbol('some_variable')
 
-    def is_field(self, proof = True):
+    cpdef bint is_field(self, proof=True) except -2:
         """
         Returns True, since the symbolic expression ring is (for the most
         part) a field.